My finding is that if you pan toward the neck pickup you can make a J sound a lot like a P. I've found this to be especially true of the Sadowsky hum-cancelling J, I guess because it has a bit of a mellower, maybe slightly hollow tone, vs. the more traditional-sounding single-coil J. Once it's in a mix, especially a dense mix like Dream Theater, and you're applying active EQ at the bass and possibly also at the amp, the difference probably won't even be discernable at all.
I use my Sadowksy 5-string J/J (hum-cancelling pickups) to play a lot of funk, soul, Motown and reggae. Most wouldn't suggest the brand for that material. A bit of passive "VTC" roll-off and old stainless strings and it sounds totally legit sonically. By far the bigger factor is my right hand than any pickup, wood, or whatever other variable you could change.
Take it with a grain of salt, as I'm not one to say "you have to hear it in a mix". Mine sounds fantastic on its own, and I've heard people playing the brand that sounded totally lost in the mix. It's really all up to you, and if you have an amp that can cop an old-school vibe or proper rock tones if you're doing metal then so much the better. So long as you don't get extreme with the active boost-only treble and bass, therefore obliterating your mids and infuriating your sound man or studio engineer, you should be fine with any quality bass of any configuration.
Speaking of which, and given anticipation over an SA-200 reissue, who plays a "modern" bass like Sadowsky through older-school style gear? Mine absolutely kills through a Mesa WalkAbout and especially a MarkBass TTE500 (their tube-style head with passive EQ stack) and a big 1x15 cab.
